Studies on Growth of Oscillation in a Class of Nonlinear Oscillator
DOI:
https://doi.org/10.32628/IJSRST1964177Keywords:
Duffing Oscillator, Rayleigh Duffing Oscillator, Nonlinear DynamicsAbstract
Growth of oscillation in Rayleigh-Duffing type oscillator has been studied using modern method of nonlinear dynamics. Primary aim is to predict the parameter range of the system where system becomes oscillatory. Analytically predicted range of system parameters are found to be in close agreement with the corresponding estimated values obtained by numerically solving system equations. This study is very helpful to explain the behaviour of a microwave Gunn oscillator and any other types of nonlinear oscillators in the free running as well as periodically driven condition.
References
- S.H.Strogatz, Nonlinear dynamics and chaos with applications to physics, chemistry and engineering, (Westview Press, Cambridge, 1994), Sec. 1:2.
- Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, Wiley, New York.
- L. Ravisankar, V. Ravichandran, and V. Chinnathambi, “Prediction of horseshoe chaos in Duffing-Van der Pol oscillator driven by different periodic forces,” International Journal of Engineering and Science, vol. 1, no. 5, pp. 17–25, 2012.
- Z. Jing, Z. Yang, and T. Jiang, “Complex dynamics in Duffing vander Pol equation,” Chaos, Solitons and Fractals, vol. 27, no. 3, pp. 722–747, 2006.
- Cao H, Seoane JM, Sanjua´n MAF. Symmetry-breaking analysis for the general Helmholtz–Duffing oscillator. Chaos, Solitons &Fractals 2007;34:197–212.
- Trueba JL, Baltana´s JP, Sanjua´n MAF. A generalized perturbed pendulum. Chaos, Solitons & Fractals 2003;15:911.
- Alberto Francescutto, Giorgio Contento, Bifurcations in ship rolling: experimental results and parameter identification technique, Ocean Engineering 26 (1999) 1095–1123.
- Alberto Francescutto, Giorgio Contento, Bifurcations in ship rolling: experimental results and parameter identification technique, Ocean Engineering 26 (1999) 1095–1123.
- Darya V. Verveyko and Andrey Yu. Verisokin, Application of He’s method to the modified Rayleigh equation,Discrete and Continuous Dynamical Systems, Supplement 2011, pp. 1423–1431.
- Pandey, M., Rand, R. and Zehnder, A., ‘Perturbation Analysis of Entrainment in a Micromechanical Limit Cycle Oscillator’, Communications in Nonlinear Science and Numerical Simulation, available online, 2006.
- Ueda Y. Randomly transitional phenomena in the system governed by Duffing’s equation. J Stat Phys 1979; 20:181.
- A.C.J. Luo, J. Huang, “Asymmetric periodic motions with chaos in a softening Duffing oscillator”, Internal Journal of Bifurcation and chaos, Vol.23, No. 5, 2013, pp-1350086(31).
- M. Siewe Siewe, H. Cao, Miguel A.F.Sanjuan "Effect of nonlinear damping on the basin boundaries of a driven two-well Rayleigh-Duffing oscillator", Chaos, Solitons and Fractals 39 (2009), 1092-1099.
- S. Munehisa, N. Inaba, T. Kawakami, "Bifurcation structure of fractional harmonic entrainments in the forced Rayleigh oscillator", Electron Commun Jpn Part 3: Fundam Electron Sci, 2004, 87, 30-40.
- M. Siewe Siew, C. Tchawoua, P. Woafo, Melnikov chaos in a periodically driven Rayleigh Duffing oscillator, Mechanics research communication, Vol.37, Issu-4, June, 2010, pp-363-368.
- B C Sarkar, C Koley, A K Guin, S Sarkar, "Some numerical and experimental observations on the growth of oscillations in an X-band Gunn oscillator", Progress In Electromagnetics Research B. 2012; 40:325-41.
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